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Famous Math & Logic Paradoxes
© Aplusclick 2016
Bermuda Triangle
Why the sum of the interior angles of the Bermuda triangle is
not 180o?
© Aplusclick 2016
Barber Paradox
In a city, the barber is the 'one who shaves all those, and
those only, who do not shave themselves.’
Who s...
Achilles and the Tortoise
The great hero Achilles challenges a tortoise to a footrace. He agrees to
give the tortoise a he...
Simpson Paradox
The average score for dance of boys and girls in class A are 16
and 21, respectively. The average score of...
Braess Paradox
The diagram shows a road network. All cars drive in one direction
from A to F. The numbers represent the ma...
Leonard Euler’s Paradox
Why the average of all of the numbers is not a zero?
1, -1, 2, -2, 3, -3, . . .
© Aplusclick 2016
Friendship Paradox
Your friends have more friends than you. Why?
© Aplusclick 2016
Uninteresting Number Paradox
How many uninteresting numbers are there?
© Aplusclick 2016
Gabriel’ Horn Paradox
The shape obtained from rotating the equation about x-axis
resembles a trumpet. If we need an infini...
Pop Quiz Paradox
A teacher announces that there will be a quiz one day during the
next week. The teacher gives the definit...
Answers at
© Aplusclick 2016
aplusclick.wordpress.com
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Famous Math and Logic Paradoxes

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Math are full of paradoxes. Many of them are simple and interesting for all of us. This is a collection of simple math and logical paradoxes from website aplusclick.com

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Famous Math and Logic Paradoxes

  1. 1. Famous Math & Logic Paradoxes © Aplusclick 2016
  2. 2. Bermuda Triangle Why the sum of the interior angles of the Bermuda triangle is not 180o? © Aplusclick 2016
  3. 3. Barber Paradox In a city, the barber is the 'one who shaves all those, and those only, who do not shave themselves.’ Who shaves the barber? © Aplusclick 2016
  4. 4. Achilles and the Tortoise The great hero Achilles challenges a tortoise to a footrace. He agrees to give the tortoise a head start of 100m. When the race begins, Achilles starts running, so that by the time he has reached the 100m mark, the tortoise has only walked 10m. But by the time Achilles has reached the 110m mark, the tortoise has walked another 1m. By the time he has reached the 111m mark, the tortoise has walked another 0.1m, then 0.01m, then 0.001m, and so on. The tortoise always moves forwards while Achilles always plays catch up. Why is Achilles always behind the tortoise? © Aplusclick 2016
  5. 5. Simpson Paradox The average score for dance of boys and girls in class A are 16 and 21, respectively. The average score of boys and girls in class B are 15 and 20, respectively. Twenty percent of class A students are girls. Forty percent of class B students are girls. Which class has a higher average score? © Aplusclick 2016
  6. 6. Braess Paradox The diagram shows a road network. All cars drive in one direction from A to F. The numbers represent the maximum flow rate in vehicles per hour. Engineers want to construct a new road with a flow rate of 100 vehicles per hour. Drivers randomly choose the road at crossroads. What new road decreases the capacity of the network (the number of vehicles at point F)? © Aplusclick 2016
  7. 7. Leonard Euler’s Paradox Why the average of all of the numbers is not a zero? 1, -1, 2, -2, 3, -3, . . . © Aplusclick 2016
  8. 8. Friendship Paradox Your friends have more friends than you. Why? © Aplusclick 2016
  9. 9. Uninteresting Number Paradox How many uninteresting numbers are there? © Aplusclick 2016
  10. 10. Gabriel’ Horn Paradox The shape obtained from rotating the equation about x-axis resembles a trumpet. If we need an infinite volume of paint to paint the infinite horn, how much paint does the horn can contain inside itself? © Aplusclick 2016
  11. 11. Pop Quiz Paradox A teacher announces that there will be a quiz one day during the next week. The teacher gives the definition that they would not when they come in to the class that the quiz was going to be given that day. The brightest student says that the quiz cannot be on Friday because they will know the day. With the same technique, she eliminates Thursday, Wednesday, Tuesday, and Monday. “You cannot give us a pop quiz next week” she says. When does the teacher give the pop quiz? I know the paradox from Charles Carter Wald. Probably, Martin Gardner described it for the first time in The Colossal Book of Mathematics. © Aplusclick 2016
  12. 12. Answers at © Aplusclick 2016 aplusclick.wordpress.com

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